The long range objectives of this research are to further the understanding of the dynamical behavior of aggregates of interacting cells and to apply this knowledge to problems of cell movement and pattern formation in developmental biology and to problems in physiology. The proposed research falls into three major categories: (l) studies on cell movement and pattern formation in Dictyostelium discoideum, (2) studies on pattern formation in limb development, and (3) studies on the dynamics of excitable media. The specific aims in (l) are: (i) to develop a model for the movement of individual cells on a substrate, both in the absence and the presence of chemotactic fields, (ii) to use the model to understand the motion of the slug stage of Dictyostelium discoideum and to explore various patterns of cell interactions that can produce tissue movement (iii) to develop a model for pattern formation and regulation in the slug stage, and (iv) to develop continuum descriptions for tissue movement. The objectives in (2) are: (i) to develop a two-dimensional model of limb development that incorporates growth and specialized regions (the AER and the ZA) on the boundary for the purpose of understanding their interaction during pattern formation in the developing limb, and (ii) to affect the patterning process and the final shape of the limb. The objectives in (3) are: (i) to study the dynamics of spiral waves in simple excitable systems in order to understand how the frequency and wavelength of the waves are set, how stable they are under various types of perturbations, and how they disappear when the excitability or rate of recovery of the medium is changed, and (ii) to study models for the dynamics of forced excitable systems with a view towards understanding the patterns of phase-locking and propagation block in spatially-distributed oscillatory or excitable systems. The work on cell movement and pattern formation in Dictyostelium discoideum will elucidate the role of cell-cell interactions, chemotaxis and cyclic AMP signalling in the motion and cell proportioning that occur in the slug stage of Dictyostelium discoideum. The work on pattern formation in limb development will further our understanding of normal development and perhaps point to the basis of various types of defects in limb development. Furthermore, the knowledge gained on that problem will contribute to our understanding of the role of growth and cell-cell interactions in the morphogenesis of other systems. The studies on excitable systems will lead to a theoretical basis for predicting fundamental properties of spiral waves, a basis that can be used in devising protocols for extinguishing such waves. These results, coupled with those on the dynamics of forced excitable systems, will expand our understanding of the origin of various types of cardiac arrythmias and how they may be prevented or controlled.